Probabilistic Operator Algebra Seminar: Conditional Bi-Free Independence

Seminar | February 13 | 3-5 p.m. | 736 Evans Hall

 Paul Skoufranis, York University, Canada

 Department of Mathematics

In this talk, we discuss the recent extension of the notion of bi-free independence to two-state systems. This so called conditional bi-free independence enables one to keep track of more information pertaining to the actions of the left and right regular representations on reduced free product spaces thereby permitting a greater number of non-commutative probabilities to be modeled. The focus of this talk will be the definition of conditional bi-free independence, the combinatorial formula for both the moment and cumulant functions, the operator-valued setting, the partial R-transforms and infinitely divisible conditional bi-free distributions.